Hall current and ion‐slip effects on free convection flow in a vertical microchannel with an induced magnetic field

Abstract

The steady fully developed hydromagnetic flow of a viscous incompressible and electrically conducting fluid in a vertical microchannel has been studied taking into account the influence of Hall current, ion-slip effects and an induced magnetic field. Exact solutions for the governing equations responsible for the flow formation are obtained by the method of the undetermined coefficient and presented graphically. It is found that in the presence of the ion-slip effect, both primary and secondary components of fluid velocity increase with the Hall parameter for symmetric as well as asymmetric heating of the microchannel surfaces. Also, the magnetic field supports flow along the secondary flow direction while the reverse impact is observed along the primary flow direction.

Computational analysis and heat transfer on MHD transient‐free convection flow in a vertical microporous channel in the existence of Hall and ion slip current

“…Hence, following Jha and Malgwi, 7 in the absence of electric current $$(\nabla \times E=0)$$ and also neglecting the effects of external pressure gradient, Joule heating, and viscous dissipation. The governing momentum, magnetic, and energy equations in the occurrence of Hall‐ion slip current and induced magnetic, describing the above assumption are presented under the usual Boussinesq approximation as $$$\frac{\partial u^{\prime} }{\partial t^{\prime} }=\upsilon \frac{{\partial }^{2}u^{\prime} }{\partial y{{\prime} }^{2}}+{v}_{0}^{^{\prime} }\frac{\partial u^{\prime} }{\partial y^{\prime} }+\frac{{\mu }_{{\rm{e}}}{H}_{0}^{^{\prime} }}{\rho }\frac{\partial {H}_{x}^{^{\prime} }}{\partial y^{\prime} }+g\beta (T^{\prime} -{T}_{0}),$$$ $$$\frac{\partial w^{\prime} }{\partial t^{\prime} }=\upsilon \frac{{\partial }^{2}w^{\prime} }{\partial y{{\prime} }^{2}}+{v}_{0}^{^{\prime} }\frac{\partial w^{\prime} }{\partial y^{\prime} }+\frac{{\mu }_{{\rm{e}}}{H}_{0}^{^{\prime} }}{\rho }\frac{\partial {H}_{z}^{^{\prime} }}{\partial y^{\prime} },$$$ …”

“…In a related article, Seth et al 5 illustrated the role of thermal diffusion and Hall current on the time‐dependent flow of chemically reactive fluid over a straight‐moving vertical wall in the occurrence of thermal radiation. Other notable articles on these important phenomena can be found in Jha et al, 6,7 Krishna, 8 and Chandrawat and Joshi 9 …”

“…Owing to the relevance of such a study, Jha and Aina 11 considered the influence of IMF on the hydromagnetic natural convection flow of Newtonian fluid in a microchannel. Furthermore, Jha and Malgwi 7,12 also investigated the role of ion slip with Hall current on MHD flow in the existence of an IMF. Dwivedi and Singh 13 highlighted the influence of IMF on point/line heat source on hydromagnetic flow in the existence of Hall current.…”

“…In a related article, Seth et al 5 illustrated the role of thermal diffusion and Hall current on the time-dependent flow of chemically reactive fluid over a straight-moving vertical wall in the occurrence of thermal radiation. Other notable articles on these important phenomena can be found in Jha et al, 6,7 Krishna, 8 and Chandrawat and Joshi. 9 On the other hand, the time-dependent theoretical examination of the problem of MHD-free convection flow of ion slip with Hall current assumes considerable attention in the occurrence of induced magnetic field (IMF) owing to its relevance in various scientific and technological applications.…”

Hall and ion‐slip effects on MHD mixed convection flow in a vertical microchannel with asymmetric wall heating

“…Rosa 19 investigated the impact of Hall and ion slip currents on nonuniform gas flows. Other related articles on the above subject includes: Jha et al, 20 Jha and Malgwi, 21‐23 Noreen et al, 24 Han et al, 25 Qureshi et al, 26 and Jha et al 27 …”